Staeckel systems generating coupled KdV hierarchies and their finite-gap and rational solutions

TL;DR

This paper introduces a method to generate coupled KdV hierarchies from Staeckel separable systems and demonstrates that their solutions include many new finite-gap and rational solutions.

Contribution

It presents a novel approach linking Staeckel systems to coupled KdV hierarchies and uncovers a large class of previously unknown solutions.

Findings

Generated new finite-gap solutions for cKdV hierarchies.

Produced a broad class of rational solutions.

Established a connection between Staeckel systems and integrable hierarchies.

Abstract

We show how to generate coupled KdV hierarchies from Staeckel separable systems of Benenti type. We further show that solutions of these Staeckel systems generate a large class of finite-gap and rational solutions of cKdV hierarchies. Most of these solutions are new.